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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="unordered.rationale"></a><a class="link" href="rationale.html" title="Implementation Rationale">Implementation Rationale</a>
</h2></div></div></div>
<p>
      The intent of this library is to implement the unordered containers in the
      draft standard, so the interface was fixed. But there are still some implementation
      decisions to make. The priorities are conformance to the standard and portability.
    </p>
<p>
      The <a href="http://en.wikipedia.org/wiki/Hash_table" target="_top">Wikipedia article
      on hash tables</a> has a good summary of the implementation issues for
      hash tables in general.
    </p>
<h3>
<a name="unordered.rationale.h0"></a>
      <span class="phrase"><a name="unordered.rationale.data_structure"></a></span><a class="link" href="rationale.html#unordered.rationale.data_structure">Data
      Structure</a>
    </h3>
<p>
      By specifying an interface for accessing the buckets of the container the standard
      pretty much requires that the hash table uses chained addressing.
    </p>
<p>
      It would be conceivable to write a hash table that uses another method. For
      example, it could use open addressing, and use the lookup chain to act as a
      bucket but there are some serious problems with this:
    </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
          The draft standard requires that pointers to elements aren't invalidated,
          so the elements can't be stored in one array, but will need a layer of
          indirection instead - losing the efficiency and most of the memory gain,
          the main advantages of open addressing.
        </li>
<li class="listitem">
          Local iterators would be very inefficient and may not be able to meet the
          complexity requirements.
        </li>
<li class="listitem">
          There are also the restrictions on when iterators can be invalidated. Since
          open addressing degrades badly when there are a high number of collisions
          the restrictions could prevent a rehash when it's really needed. The maximum
          load factor could be set to a fairly low value to work around this - but
          the standard requires that it is initially set to 1.0.
        </li>
<li class="listitem">
          And since the standard is written with a eye towards chained addressing,
          users will be surprised if the performance doesn't reflect that.
        </li>
</ul></div>
<p>
      So chained addressing is used.
    </p>
<h3>
<a name="unordered.rationale.h1"></a>
      <span class="phrase"><a name="unordered.rationale.number_of_buckets"></a></span><a class="link" href="rationale.html#unordered.rationale.number_of_buckets">Number
      of Buckets</a>
    </h3>
<p>
      There are two popular methods for choosing the number of buckets in a hash
      table. One is to have a prime number of buckets, another is to use a power
      of 2.
    </p>
<p>
      Using a prime number of buckets, and choosing a bucket by using the modulus
      of the hash function's result will usually give a good result. The downside
      is that the required modulus operation is fairly expensive. This is what the
      containers do in most cases.
    </p>
<p>
      Using a power of 2 allows for much quicker selection of the bucket to use,
      but at the expense of losing the upper bits of the hash value. For some specially
      designed hash functions it is possible to do this and still get a good result
      but as the containers can take arbitrary hash functions this can't be relied
      on.
    </p>
<p>
      To avoid this a transformation could be applied to the hash function, for an
      example see <a href="http://web.archive.org/web/20121102023700/http://www.concentric.net/~Ttwang/tech/inthash.htm" target="_top">Thomas
      Wang's article on integer hash functions</a>. Unfortunately, a transformation
      like Wang's requires knowledge of the number of bits in the hash value, so
      it isn't portable enough to use as a default. It can applicable in certain
      cases so the containers have a policy based implementation that can use this
      alternative technique.
    </p>
<p>
      Currently this is only done on 64 bit architectures, where prime number modulus
      can be expensive. Although this varies depending on the architecture, so I
      probably should revisit it.
    </p>
<p>
      I'm also thinking of introducing a mechanism whereby a hash function can indicate
      that it's safe to be used directly with power of 2 buckets, in which case a
      faster plain power of 2 implementation can be used.
    </p>
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<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
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<td align="right"><div class="copyright-footer">Copyright © 2003, 2004 Jeremy B. Maitin-Shepard<br>Copyright © 2005-2008 Daniel
      James<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
      </p>
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